Compensation for measurement uncertainty due to atmospheric effects

ABSTRACT

An apparatus and method for compensating for measurement uncertainty due to atmospheric effects. In one embodiment the apparatus includes two sources separated by a predetermined distance and two target locations separated by a predetermined distance. The radiation at the target locations is combined to form an interference pattern onto a detector which generates a signal corresponding to the measurement having a substantially reduced error due to atmospheric effects such as temperature variations. In another embodiment the radiation from the sources crosses somewhere in the measurement environment as it propagates toward the target locations. In yet another embodiment the separation between the two sources is substantially the same as the separation between the two target locations.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 09/241,354 which was filed on Feb. 2, 1999 now U.S. Pat. No.6,031,612 which was a continuation-in-part of U.S. patent applicationSer. No. 08/600,216 now U.S. Pat. No. 5,870,191 which was filed on Feb.12, 1996 and claims priority to provisional U.S. patent application No.60/087,960 which was filed Jun. 4, 1998.

GOVERNMENT SUPPORT

Work described herein was supported by Federal Contract No.F19628-95-L-002, awarded by the United States Air Force. The Governmentmay have certain rights in the invention.

FIELD OF THE INVENTION

The invention relates to the field of metrology, and more specificallyto optical non-contact position measurement.

BACKGROUND OF THE INVENTION

Precise non-contact measurement of the deformation or displacement ofobjects is critical when active or passive compensation for thedeformation or displacement is required. For example, large parabolicdishes used for communication, radar or telescopes are susceptible tomany natural influences which distort the shape of the dishes. Some ofthese natural influences include wind, gravitational forces which cancause the dish to sag depending on the orientation of the dish, andtemperature variations in the dish which can distort the shape of thedish, etc. To compensate for these effects, several solutions may beemployed. One such solution is to use mechanical actuators on asegmented dish with an array of detectors mounted in different locationson the dish. As the detectors sense a change in the shape of the dish,the actuators respond by moving segments of the dish to correct theshape of the dish. A large disadvantage of this technique is the amountof cables and other electrical components which need to be mounted tothe dish to perform the compensation. Another solution involves usingmathematical techniques to correct the received signal as reflected bythe deformed surface. This technique is of limited usefulness since thedistortions in the dish are typically not uniform and cannot always beaccurately modeled. These measurements can also be applied to otherstructures where deformations are studied, such as building surfaces,airplane surfaces, space shuttle surfaces, and surfaces of automobiles.In each case, the amount of surface deformation must be accuratelymeasured so that the correct amount of compensation can be applied.These measurements can effect the design of wings on an airplane or therear spoiler on a racing car, for example.

Other techniques for measuring deformations in the surface of objectsinclude using laser range finders which provide precise measurementinformation. Typically it is cost prohibitive to use many of these laserrange finders to simultaneously measure many points on the surface. Morepractically these range finders are used for individual sequentialmeasurements at different points on the surface of the object. Hence,the measurements are not made simultaneously. Also, these laser rangefinders are sensitive to temperature changes in the atmosphere along thez-axis in FIG. 1. Temperature variations between the left side of FIG. 1and the right side of FIG. 1, or bulk temperature changes along theentire path L can severely compromise the measurement accuracy of theselaser trackers.

Another measurement technique projects a fringe pattern on a detectorwhich is mounted to the surface to be measured. As the surface deforms,the detector moves and sweeps across the fringe pattern. By detectingthe changes in the light intensity, the deformation of the surface canbe determined. Although this technique provides a relatively inexpensiveway to simultaneously detect relative displacement of a surface, it issensitive to temperature variations in the atmosphere as well, but inthe direction of the x-axis in FIG. 1. In other words, the temperaturesensitivity of this technique is to temperature variations in thedirection displacements are being measured. Therefore, this measurementtechnique is sensitive to temperature gradients. Those gradients resultin shifts in the fringe pattern at the detector independent of therelative motion of the detector and the fringe pattern. Note that thistechnique is not sensitive to temperature variations along the z-axis asshown in FIG. 1.

These optical techniques are susceptible to temperature variations inthe atmosphere because those temperature changes cause index ofrefraction variations. These index of refraction variations cause lighttraveling through the atmosphere to bend. The amount of this bendingdepends on the severity of the refractive index variations. Themeasurement techniques discussed above do not compensate for theserefractive index variations. Thus, the measurement result is not asprecise as it would be without refractive index variations in theatmosphere. Therefore, non-contact techniques for measuring surfacedeformation or distortion cannot identify whether the distortion is dueto the wind, gravity, or atmospheric effects affecting the measurementequipment.

The present invention provides a method and apparatus for compensatingfor atmospheric effects that typically plague measurement equipment. Thetechnique is useful in precise non-contact measurement of surfacedistortion without adding the uncertainty of refractive index changes inthe atmosphere. The technique could also be used in precision landsurveying, to aid in the building of a linear accelerator, or anysituation where precise straightness measurements are required. Thetechnique may be used to compensate for measurement uncertainty due toatmospheric refractive index effects.

SUMMARY OF THE INVENTION

The invention relates to an apparatus and method for compensating formeasurement error due to refractive index variations in the measurementenvironment. In one embodiment the apparatus includes two sourcesseparated by a predetermined distance and two target locations separatedby a predetermined distance. The radiation at the target locations iscombined to form an interference pattern onto a detector which generatesa signal which corresponds to the measurement having substantiallyreduced error due to refractive index variations in the measurementenvironment. In another embodiment, the radiation from the two sourcescrosses somewhere in the measurement environment before reaching the twotarget locations. In yet another embodiment, the distance separating thetwo sources is substantially equal to the distance separating the twotarget locations. In yet another embodiment, the two sources aregenerated from a single source. The source(s) could be broadband orlaser.

In one embodiment, the two sources and the two target locations aresubstantially adjacent to each other. The radiation from the sources isdirected back from a target reflector towards the sources and iscombined to form an interference pattern onto a detector which generatesa signal which corresponds to the measurement having substantiallyreduced error due to refractive index variations in the measurementenvironment.

BRIEF DESCRIPTION OF THE DRAWINGS

This invention is pointed out with particularity in the appended claims.The above and further advantages of this invention may be betterunderstood by referring to the following description taken inconjunction with the accompanying drawings, in which:

FIG. 1 is an embodiment of a measurement system which uses a measurementtechnique known to the prior art.

FIG. 2 is ray trace diagram of an embodiment of the invention.

FIG. 3 is a diagram of an embodiment of the present invention usingpolarization tracking.

FIG. 4 is a highly schematic diagram of another embodiment of theinvention.

FIG. 5 is a highly schematic diagram of still another embodiment of theinvention.

FIG. 6a is a highly schematic diagram of yet another embodiment of theinvention.

FIG. 6b is a highly schematic diagram of still another embodiment of theinvention.

FIG. 7a is a graph of simulated random temperature gradients in asimulated measurement environment.

FIG. 7b is a graph of simulated measurement error due to the simulatedrandom temperature gradients of FIG. 7a for both conventionalmeasurement and reduced error measurement according to the invention.

FIG. 8 is a graph of the measurement error for both conventionalmeasurement and reduced error measurement using the embodiment of theinvention shown in FIG. 5.

DETAILED DESCRIPTION OF THE INVENTION

In brief overview and referring to FIG. 1, one prior art measurementtechnique for measuring displacement of the surface of an object isshown. In order to measure the displacement of a point 10 on thedetector 12, two sources of radiation 2, 2′ can be used. The two sourcesof radiation 2, 2′ must be coherent with respect to one another. As thetwo sources of radiation 2, 2′ irradiate the detector 12, they producean interference pattern 16 on the detector 12. The interference pattern16 consists of regions of varying intensity 18, 18′; each regionrepresents a fringe period of the repeated interference pattern 16. Asthe point 10 is displaced in the x direction, the detector 12 senses themovement of the point 10 with respect to the interference pattern 16.The detector 12 is sensitive to the intensity variations of the fringesso it can detect movement within the same fringe period. The detector 12can also detect movement through whole fringe periods so determininglarger displacements of the point 10 is relatively straightforward andinvolves counting fringe periods as they pass over the detector 12.

Although the technique described above can measure the relativedisplacement of the point 10, it cannot identify whether the fringeshifts were due to the actual displacement of the detector or due toatmospheric effects, or a combination of the two. This is because as thetemperature changes in the measurement environment (i.e. theatmosphere), so does the refractive index of the environment and thebeams 4 and 6 will refract differently in the changing temperatureenvironment. This beam refraction will shift the interference pattern 16on the detector 12. The detector 12 will thereby sense a false change inthe displacement of point 10 and report that artificial displacementcausing the measurement to be imprecise.

Turning again to FIG. 1, the optical path length difference betweenbeams s₁ and s₂ is described by the equation:

OPD=s ₂ −s ₁   (1)

where s₁ and s₂ are optical path lengths that involve the integral ofthe path length multiplied by the refractive index at each point alongthe length.

In a uniform temperature gradient in the x direction, this can also berepresented by the expansion:

OPD≈(an ₀ /L)x ₀−(P ₀ L/2)a+  (2)

where P₀ represents the uniform temperature gradient described as thederivative of the refractive index (n) with respect to the x direction,substantially perpendicular to a bisector of the sources 2, 2′. The termP₀ is difficult to ascertain. The nominal refractive index in themeasurement environment is n₀. The distance between the sources 2, 2′ isa, and L is the distance between the z=0 plane of the sources 2, 2′ andthe z=L plane of the target locations 20, 20′. The term x₀ is theunknown displacement. The higher order terms in equation 2 havenegligible effect and can be ignored when a is much less than L. Thefirst term in equation 2 consists of known quantities except for x₀which is the unknown displacement. The second term in the equationincludes the term P₀ which as discussed above is the derivative of nwith respect to the x direction. That is, this term represents thechange in refractive index with respect to x and is difficult todiscern.

Referring now to FIG. 2, one embodiment of the invention includes twomutually coherent light sources 2, 2′ separated by a distance a whichirradiate two target locations 20, 20′ located a distance L from thesources 2, 2′. The two light sources 2, 2′ may be generated from asingle source and also may be broadband or laser sources. An opticalcombiner 24 in communication with the target locations 20, 20′, directsthe beams 22, 22′ to the detector 12. The beams 22, 22′ will combine atthe location of the detector 12 to produce an interference pattern 16.The detector 12 is sensitive to intensity variations of the fringes soit can detect movement within the same fringe period. The detector 12can also detect movement through whole fringe periods so determining thedisplacement of the point 10 is relatively straightforward and involvessimply the counting of the passing fringe periods. In another embodimentof the invention, multiple detectors may be used including arraydetectors. By choosing a suitable separation a of the two sources 2, 2′and a suitable separation b of the two target locations 20, 20′, where bis defined as the difference between the x-value at target location 20and the x-value at target location 20′ (for example, b is positive asdrawn in FIG. 2), the atmospheric term in equation 2 above will beremoved from the equation, for a =b. The equation for the OPDcorresponding to FIG. 2 is:

OPD≈(an ₀ /L)X ₀−(P ₀ L/2)(a−b)   (3)

In a uniform temperature gradient, the atmospheric refraction errorbeing accumulated is proportional to the distance between two points atthe same z-location on two beam paths 22 and 22′. For example, thedistance between the sources is, so the error being accumulated at z=0is proportional to the distance. The reason for this is that the changein refractive index is proportional to the linear temperature gradient.Moving towards the center, the distance between the points on the beampaths 22 and 22′ is less, and therefore the accumulated error is less.Reaching point 21 where the beams cross, the error is zero. Moving tothe other side of the crossing point 21, the upper beam now becomes thelower beam and the lower beam becomes the upper beam. The error is nowbeing accumulated in the opposite direction since the beams areswitched. Since the gradient is uniform across the length L, the errorthat was accumulated on the left side of crossing point 21 is exactlyundone by the opposite accumulation on the right side of crossing point21. Therefore, when the separation a between the two sources 2, 2′ isequal to the separation b between the two target locations 20, 20′, theeffect of the uniform temperature gradient is canceled. Hence, a isequal to b. In other words, this embodiment of the invention haseffectively compensated for atmospheric effects due to a uniformtemperature gradient 8 in the measurement environment. Therefore the OPDis given by the equation:

Opd≈(an ₀ /L)x ₀   (4)

in which all quantities except x₀ are known.

In certain circumstances it may be desirable to change the separationbetween the two sources 2, 2′ or the two target locations 20, 20′. Thiswill actually allow for the tuning of the apparatus to more effectivelycompensate for non-uniform temperature gradients.

Because both sources may irradiate both target locations, a techniquemust be used to differentiate which beams came from which source. Thisis required since the invention takes advantage of the geometry of thesources and the detectors in order to compensate for the atmospherictemperature gradient. In one embodiment, radiation from source 2′ isdirected at target 20, while radiation from source 2 is directed attarget 20′. In this embodiment, the beams cross somewhere in themeasurement environment. In order to manipulate the beams according tothe invention, the source and the target of the radiation must be known.

This beam tracking can be done in various ways. For example, in oneembodiment of the invention, narrow coherent lasers may be used assources 2, 2′, each could be directed to irradiate only one targetlocation 20 or 20′. Another embodiment of the invention usespolarization as shown in FIG. 3. Linear polarizers 28, 30 are orthogonalwith respect to one another. Radiation from source 2 is directed intopolarizer 28 allowing only linearly polarized light 22 to reach targetlocation 20′. Radiation from source 2′ is directed into polarizer 30allowing only linearly polarized light 22′ to reach target location 20.The two beams 22 and 22′ are orthogonally polarized with respect to oneanother. Before these beams 22, 22′ interfere and reach the detector,they pass through analyzers 32, 34, which are linearly polarized in thesame orientation of the beams 22, 22′. This technique allows only thebeam from the correct source 2, 2′ to reach each target location 20, 20′and thereby produces a desired condition (for example, a =b ) inequation 3. In this embodiment, analyzer 26 is positioned just beforethe detector 12 to cause the cross polarized beams to interfere. Inanother embodiment according to FIG. 4, calcite 38 or another suitablematerial can be used to separate the beams into orthogonally polarizedcomponents and recombine the beams from such components.

In FIG. 4, source 36, which can be a broadband or laser source, directsradiation into crystal 38, which can be calcite or any other suitablebirefringent material. Birefringent crystal 38 divides and diverts theradiation internally and produces extraordinary beam 40 and ordinarybeam 42. Beams 40 and 42 become virtual sources 2 and 2′ as they leavethe crystal 38. Beams 22 and 22′ are orthogonally polarized with respectto one another. As beams 22 and 22′ propagate, they eventually encountera detection birefringent crystal 44 which performs the function ofrecombining the beams in such a way as to produce an interferencepattern on detector 12 after the beams traverse analyzer 26.

FIG. 5 depicts another embodiment of the invention. Since it may not bedesirable to mount electronics and cables on the surface of the object,FIG. 5 illustrates an embodiment of the invention that addresses thatissue. Here the analyzer 26 and the detector 12 are substantiallyadjacent to the source 36. A beam splitter 60 is positioned to allowradiation from source 36 to enter crystal 38 which generates beams 22and 22′ as above. Crystal 38 is a birefringent crystal which splits thepolarization between beams 40 and 42. Beams 40 and 42 exit the crystal38 and propagate as 22, 22′ until they reach a target reflector 50. Thetarget reflector in one embodiment is a polarizing beam splitter.Retro-reflectors 52 and 54, which may be corner cubes, are used todirect the beams 58 and 56 back to beam splitter 60. The separation bmay be changed by adjusting retro-reflectors 52 and 54. This allowstuning of the apparatus for non-uniform temperature gradients. Beamsplitter 60 directs the beams 22, 22′ through the analyzer 26 to producean interference pattern at detector 12. The analyzer 26 in oneembodiment is a polarizer.

FIGS. 6a and 6 b illustrate alternate embodiments of the invention.Turning to FIG. 6a, it can be shown that by taking two measurements fordifferent values of b (for example b=0 and b=−a), the P₀ term inequation 3 can be eliminated. The physical apparatus may include twosources, or a single source 36 and two virtual sources 2, 2′. Theapparatus also includes optical combiner 24, analyzer 26, and a detector12. The apparatus may use multiple detectors including array detectors.Note that when using the polarization technique to track the beams asshown in the FIG. 6a embodiment of the invention, the axes of theanalyzers 32 and 34 in FIG. 3 must be switched, since the beams are notcrossed in the measurement environment. Moreover, with reference to FIG.6a, depending on which beams from virtual sources 2 and 2′ are tracked,it is possible to achieve the desired result of atmospheric refractioncompensation with or without crossing the beams in the measurementenvironment.

In the embodiment of the invention as shown in FIG. 6a, beams 22 and 22′do not cross in the measurement environment. Source 36, which could be abroadband source or a laser source, illuminates crystal 38. Beams 22 and22′ are orthogonally polarized with respect to one another. As beams 22and 22′ propagate they are directed to optical combiner 24. As opticalcombiner 24 combines the beams, they pass through analyzer 26, which canbe a polarizer, before producing an interference pattern on detector 12.Alternatively, as shown in FIG. 6b, multiple crossing points may bedesirable and can be achieved by using reflectors 66, 68, 70, and 72 andcrystal 44. In this embodiment, beams 23 and 23′ propagate through themeasurement environment and eventually reach crystal 44, where they arerecombined, pass through an analyzer 26, and produce an interferencepattern on detector 12. Again, by manipulating the beams 23, 23′, thedesired condition of atmospheric compensation can be satisfied.

FIGS. 7a and 7 b are graphs of the simulated results observed for randomtemperature gradients using the invention. The purpose of the simulationis to show that there is effective compensation even though thegradients in FIG. 7a are not exactly uniform. Simulated measurementswere taken using a conventional measurement technique. The call-outnumbers in FIG. 7a correspond to the realization numbers in FIG. 7b. Theresults of simulated conventional measurements are shown by the dottedlines in FIG. 7b. Simulated measurements using the invention are shownin FIG. 7b as solid lines. Note that the solid lines indicating themeasurement error show less error in the measurement using theinvention.

FIG. 8 shows actual measurement results for the embodiment of theinvention shown in FIG. 5. As indicated in the FIG. 8, when heaters wereactivated in the measurement environment the technique used by theinvention showed dramatic improvement in measurement accuracy.

Having described and shown the preferred embodiments of the invention,it will now become apparent to one of skill in the art that otherembodiments incorporating the concepts may be used and that manyvariations are possible which will still be within the scope and spiritof the claimed invention. It is felt, therefore, that these embodimentsshould not be limited to disclosed embodiments but rather should belimited only by the spirit and scope of the following claims.

What is claimed is:
 1. A method for compensating for measurement errordue to refractive index variations in a measurement environment, saidmethod comprising the steps of: providing a first source of radiationand a second source of radiation, said first source of radiation andsaid second source of radiation being separated by a first predetermineddistance; irradiating a first target location with radiation from saidfirst source of radiation through said refractive index variations insaid measurement environment; irradiating a second target location withradiation from said second source of radiation through said refractiveindex variations in said measurement environment, said second targetlocation separated from said first target location by a secondpredetermined distance; combining said radiation from said first andsecond target locations to generate optical interference at a thirdtarget location; and detecting radiation at said third target locationto generate a signal having substantially reduced measurement error dueto said refractive index variations in said measurement environment. 2.The method of claim 1 wherein said first and second sources are coherentwith respect to one another.
 3. The method of claim 1 wherein said firstpredetermined distance and said second predetermined distance aresubstantially equal.
 4. The method of claim 1 wherein said first andsecond sources of radiation have a first wavelength and wherein saidfirst predetermined distance is substantially proportional to said firstwavelength of radiation from said first and second sources of radiation.5. The method of claim 1 wherein said first and second sources aregenerated from a single source.
 6. The method of claim 5 wherein saidsingle source is a laser source.
 7. The method of claim 1 wherein saidfirst target location and said second target location are transposed. 8.The method of claim 1 wherein said refractive index variations are dueto spatial temperature variations in the measurement environment.
 9. Themethod of claim 1 wherein said first and second sources are lasersources.
 10. The method of claim 1 wherein said first and second sourcesare broadband sources.
 11. An apparatus for compensating for measurementerror due to refractive index variations in a measurement environment,said apparatus comprising: a first source of radiation irradiating afirst target location through said refractive index variations in saidmeasurement environment; a second source of radiation irradiating asecond target location through said refractive index variations in saidmeasurement environment, said first and second sources of radiationseparated by a first predetermined distance, said first and secondtarget locations separated by a second predetermined distance; anoptical combiner in optical communication with said first and secondtarget locations; and a detector in optical communication with saidoptical combiner; wherein said optical combiner directs radiation fromsaid first and second target locations to said detector, said detectorgenerating a signal having substantially reduced measurement error dueto said refractive index variations in said measurement environment. 12.The apparatus of claim 11 wherein said first and second sources aregenerated from a single source.
 13. The apparatus of claim 12 whereinsaid single source is a laser source.
 14. The apparatus of claim 11wherein said first predetermined distance and said second predetermineddistance is substantially the same.
 15. The apparatus of claim 11wherein said refractive index variations are due to spatial temperaturevariations in the measurement environment.
 16. The apparatus of claim 11wherein said first and second sources are laser sources.
 17. Theapparatus of claim 11 wherein said first and second sources arebroadband sources.
 18. The apparatus of claim 11 wherein said detectoris located substantially adjacent to said first and second sources. 19.The apparatus of claim 18 further comprising an optical component incommunication with said first and second sources and said opticalcombiner, said optical component directing radiation from said first andsecond target locations to said detector.
 20. The method of claim 1,wherein said radiation from said first source of radiation intersectssaid radiation from said second source of radiation exactly once priorto irradiating said first and second target locations, respectively. 21.The method of claim 1, wherein said radiation from said first source ofradiation intersects said radiation from said second source of radiationmore than once prior to irradiating said first and second targetlocations, respectively.
 22. The method of claim 1, wherein saidradiation from said first source of radiation does not intersect saidradiation from said second source of radiation prior to irradiating saidfirst and second target locations, respectively.
 23. The method of claim1, wherein said step of detecting radiation at said third targetlocation comprises reflecting said radiation from said first and secondtarget locations.
 24. The method of claim 23, wherein said step ofdetecting radiation at said third target location comprises detectingsaid radiation proximate to said first and second sources.
 25. Themethod of claim 1, wherein said step of combining said radiationcomprises reflecting said radiation from said first and second targetlocations prior to combining said radiation to generate opticalinterference at said third target location.
 26. The method of claim 1,wherein said third target location is proximate to said first and secondsources of radiation.
 27. The apparatus of claim 11, wherein saidradiation from said first source of radiation intersects said radiationfrom said second source of radiation exactly once prior to irradiatingsaid first and second target locations, respectively.
 28. The apparatusof claim 11, wherein said radiation from said first source of radiationintersects said radiation from said second source of radiation more thanonce prior to irradiating said first and second target locations,respectively.
 29. The apparatus of claim 11, wherein said radiation fromsaid first source of radiation does not intersect said radiation fromsaid second source of radiation exactly once prior to irradiating saidfirst and second target locations, respectively.
 30. The apparatus ofclaim 11, wherein said optical combiner receives radiation from saidfirst and second target locations.
 31. The apparatus of claim 11,wherein said optical combiner receives radiation reflected from saidfirst and second target locations.
 32. The apparatus of claim 31,wherein said optical combiner is located proximate to said first andsecond sources.
 33. The apparatus of claim 11, wherein said first targetlocation and said second target location are transposed.
 34. Theapparatus of claim 11, wherein said detector comprises a photodetector.